A gaming device that has an award modification function for player selectable awards that may be implemented with a primary or bonus game. More specifically, a processor controlled gaming device randomly generates a plurality of positions or digits of an award and enables the player to pick which position or digit receives a first randomly generated number, which digit receives a second randomly generated number, etc., until each of the positions have a number, whereby the gaming device determines the player's ultimate award. A plurality of modification methods can be employed to individually modify the digits of the award.